Meson-meson interaction in the Bethe-Salpeter approximation

Abstract

The π-π interaction is studied in the Bethe-Salpeter approximation by first obtaining the "effective" interaction Hamiltonian with the help of the lowest order S matrix for π-π scattering. This Hamiltonian is then used to set up a Goldberger-type integral equation for π-π scattering which is solved for the cases of total isotopic spins I=0, 2, assuming the mesons to be in s states with respect to each other. It is found that the interaction in the state I=0 is too strongly attractive to give a resonance. On the other hand, a resonance is obtained for the case I=2, at a momentum (in the center-of-mass system) k∼93 Mev/c for each meson, taking G²/4π=15.5.